Eleven seats on a condominium association board for buildings Amity, Buddy, and Chum are to be apportioned.

Current Representation:
Amity Buddy Chum
1 800 2113 4050
2 267 704 1350
3 133 352 675
4 80 211 405
5 53 141 270

Use the given table of Huntington-Hill numbers to list the order in which the seats on the board will be apportioned. For example: ABCCABABC

How do I list the order? I do not know how to do this problem.

To list the order of seats on the board using the Huntington-Hill method, you will need to follow these steps:

Step 1: Calculate the Priorities
- First, calculate the priority for each building based on their current representation. The priority formula is sqrt(N(N + 1)), where N is the current representation.
- Calculate the priority for each building (Amity, Buddy, and Chum) using the given table:

Current Representation:
Amity:
1: 800
2: 267
3: 133
4: 80
5: 53

Buddy:
1: 2113
2: 704
3: 352
4: 211
5: 141

Chum:
1: 4050
2: 1350
3: 675
4: 405
5: 270

- Use the formula sqrt(N(N + 1)) to calculate the priority for each building at each representation level.

Step 2: Calculate the Standard Divisor
- To calculate the standard divisor, use the formula:
SD = Total Population / sqrt(1 * 2 * 3 * ... * n)
where Total Population is the sum of the representation for all buildings and n is the number of seats to be apportioned.

- Calculate the total population and the standard divisor using the given representation table.

Step 3: Calculate the Quotas
- Calculate the quota for each building at each representation level using the formula:
Quota = Priority / SD
Round the quota down to the nearest whole number.

Step 4: Calculate the Priorities Adjusted Quotas
- Calculate the priority-adjusted quota for each building at each representation level using the formula:
Priority-Adjusted Quota = Priority * Quota
Round the priority-adjusted quota down to the nearest whole number.

Step 5: Calculate the Final Quotas
- Calculate the final quota for each building at each representation level using the formula:
Final Quota = Priority-Adjusted Quota / Quota
Round the final quota to the nearest whole number.

Step 6: Determine the Apportionment Order
- Determine the order of apportionment by sorting the final quotas in decreasing order.
- Start with the building that has the highest final quota and continue in descending order.

Using the formulas and steps listed above, you can now calculate the order in which the seats on the board will be apportioned.